Title: Conditional graphical modeling of multivariate functional data
Authors: Kuang-Yao Lee - Temple University (United States) [presenting]
Dingjue Ji - Yale (United States)
Lexin Li - University of California Berkeley (United States)
Todd Constable - Yale (United States)
Hongyu Zhao - Yale University (United States)
Abstract: Graphical modeling of multivariate functional data is becoming increasingly important in a wide variety of applications. Most existing methods focus on estimating the graph by aggregating samples, but largely ignore the subject-level heterogeneity, which can often be attributed to some external variables. We introduce a conditional graphical model for multivariate random functions, where we treat the external variables as conditioning set and allow the graph structure to vary with the external variables. Our method is built on two new linear operators, the conditional precision operator and the conditional partial correlation operator, which extend the precision matrix and the partial correlation matrix to both the conditional and functional settings. We show their nonzero elements can be used to characterize the conditional graphs, and develop the corresponding estimators. We establish the uniform convergence of the proposed estimators and the consistency of the estimated graph. At the same time, we allow the graph size to grow with the sample size and accommodate both completely and partially observed data. We demonstrate the efficacy of the method through both simulations and a study of brain functional connectivity network.